An Invariant Approach to Adaptive Radar Detection Under Covariance Persymmetry

In this paper, we propose a systematic and unifying framework to deal with adaptive radar detection in the presence of Gaussian interference sharing a persymmetric covariance structure. First, we determine the group of transformations which leaves the considered hypothesis testing problem unaltered; then, after reduction by sufficiency, we determine a maximal invariant statistic which is a four dimensional vector and significantly compresses the original observation space. Its first two components are the one-step and the two-step Generalized Likelihood Ratio Test decision statistics respectively, whereas its last two entries represent an ancillary statistic. We provide also the exact statistical characterization of the maximal invariant which is exploited to synthesize both the optimum and the locally optimum (in the low Signal-to-Interference-plus-Noise Ratio regime) invariant receivers. Finally, some sub-optimum decision rules based on theoretically solid design criteria are discussed and their performances are analyzed in comparison with the benchmark invariant test.